Naturalness Under Stress

Naturalness has for many years been a guiding principle in the search for physics beyond the Standard Model, particularly for understanding the physics of electroweak symmetry breaking. However, the discovery of the Higgs particle at 125 GeV, accompanied by the exclusion of many types of new physics expected in natural models, has called the principle into question. In addition, apart from the scale of weak interactions, there are other quantities in nature that appear unnaturally small and for which we have no proposal for a natural explanation. I first review the principle, then discuss some of the conjectures it has spawned. I then turn to some of the challenges to the naturalness idea and consider alternatives.